U.S. patent application number 14/712872 was filed with the patent office on 2016-11-17 for spectrum-efficient secondary users grouping method for two-tier cognitive radio networks.
The applicant listed for this patent is KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS. Invention is credited to YOUSEF NAIEF SHNAIWER, SALAM ADEL ZUMMO.
Application Number | 20160338030 14/712872 |
Document ID | / |
Family ID | 57276316 |
Filed Date | 2016-11-17 |
United States Patent
Application |
20160338030 |
Kind Code |
A1 |
SHNAIWER; YOUSEF NAIEF ; et
al. |
November 17, 2016 |
SPECTRUM-EFFICIENT SECONDARY USERS GROUPING METHOD FOR TWO-TIER
COGNITIVE RADIO NETWORKS
Abstract
The spectrum-efficient secondary users grouping method for
two-tier cognitive radio groups femtocell base stations (FBSs) and
macrocell secondary users (MSUs) into non-interfering groups based
on their GPS location information, and then serves the FBSs/MSUs
within each group using the same channel. A first approach for
grouping the secondary users (SUs) is distance-based. A second
approach utilizes profit maximization. Both approaches are extended
to a co-channel deployment scenario where the FBSs can share part
of the channels purchased for the MSUs to further reduce the number
of channels to be purchased from the PU networks. The
distance-based grouping method finds the minimum number of groups
such that the desired quality of service (QoS) determined by an
outage probability threshold is maintained. The profit maximization
method tries to find the set of SUs that maximizes the expected
total profit of the SU network.
Inventors: |
SHNAIWER; YOUSEF NAIEF;
(DHAHRAN, SA) ; ZUMMO; SALAM ADEL; (DHAHRAN,
SA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS |
DHAHRAN |
|
SA |
|
|
Family ID: |
57276316 |
Appl. No.: |
14/712872 |
Filed: |
May 14, 2015 |
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H04W 16/14 20130101;
H04W 64/003 20130101; H04W 72/082 20130101; H04W 24/02
20130101 |
International
Class: |
H04W 72/04 20060101
H04W072/04; H04L 12/26 20060101 H04L012/26 |
Claims
1. A spectrum-efficient secondary users grouping method for
two-tier cognitive radio networks, comprising the steps of:
grouping femtocell base stations (FBSs) and macrocell secondary
users (MSUs) into non-interfering groups based on their location
information, the grouping being performed by a cognitive base
station (CBS); and serving the FBSs/MSUs within each of the groups
using a common channel, the common channel being purchased by the
CBS.
2. The spectrum-efficient secondary users grouping method according
to claim 1, wherein the grouping is distance-based.
3. The spectrum-efficient secondary users grouping method according
to claim 2, further comprising the steps of: determining an outage
probability threshold; establishing a desired quality of service
(QoS); and finding a minimum number of the groups capable of
maintaining the desired quality of service.
4. The spectrum-efficient secondary users grouping method according
to claim 2, wherein said distance-based grouping further comprises
the step of using the distance between an FBS inside an FSU's
femtocell and an FBS in another femtocell in order to approximate a
distance between the FSU and the FBS in the other femtocell.
5. The spectrum-efficient secondary users grouping method according
to claim 2, further comprising the step of implementing a distance
threshold minimization based on a worst-case interference
assumption in the network.
6. The spectrum-efficient secondary users grouping method according
to claim 5, further comprising the steps of: (a) each of the FBSs
sending its location to the CBS; (b) storing distances between the
femtocells, the distances being based on the FBS locations sent to
the CBS; (c) assigning a first ungrouped FBS to a group; (d)
storing a number of FSUs served by the first ungrouped FBS as a
category of the group, the category being defined as a maximum
allowed number of FSUs per FBS member, thereby corresponding to a
number of channels needed to be assigned by the group; (e) for a
subsequent ungrouped FBS, assigning it to the group if the distance
between the subsequent ungrouped FBS and the first ungrouped FBS is
larger than a distance threshold D.sub.th and the number of FSUs
served by the subsequent ungrouped FBS is less than or equal to the
category of the group; and (f) repeating steps (c) through (e) for
first and subsequent ungrouped FBS until all the FBSs have been
grouped.
7. The spectrum-efficient secondary users grouping method according
to claim 6, further comprising the step of using a minimum said
distance threshold D.sub.th satisfying the desired quality of
service (QoS).
8. The spectrum-efficient secondary users grouping method according
to claim 6, further comprising the steps of: for each of said
groups, first assigning to D.sub.th a distance double an FBS radius
(2R.sub.F); based on the distances between the FBSs, the CBS
finding the expected uplink outage probability at each of the FBSs
assigned to the group according to: P out ( k ) = s = 1 S [ P out |
s ( k ) .times. p ks ] = s = 1 S s i = 1 s - 1 [ 1 - ( Pr { D
.gtoreq. D th } ) M i Pr { N k .ltoreq. C i } ] .times. ( Pr { D
.gtoreq. D th } ) M s Pr { N k .ltoreq. C s } .times. P out | s ( k
) , ##EQU00025## where P.sub.out.sup.(k) is an outage probability
given that the FSU under consideration is utilizing the channel
assigned to Group s (depends on the number of the members of Group
s, and on their distances from the k.sup.th FBS), s is a group
search range, D.sub.th is a distance threshold, D is an actual
distance, N.sub.k is the number of users served by FBS k, C.sub.s
is the category of group s, M.sub.s is the number of members in
group s, M.sub.i is the number of members in group i, p.sub.ks is
the probability that the k.sup.th FBS is assigned to Group s, and
P.sub.out|s.sup.(k) is the outage probability; the CBS comparing
the maximum uplink outage probability with a target maximum uplink
outage probability; the CBS choosing R.sub.F as D.sub.th if the
maximum uplink outage probability is smaller than the target; if
the maximum uplink outage probability is larger than the target,
the CBS incrementing the value of D.sub.th while performing
grouping until the maximum uplink outage probability becomes lower
than the target, the CBS then fixing the last two values of
D.sub.th as the desired range; and the CBS applying a bisection
method on the desired range to find the optimum value of D.sub.th
for that group.
9. The spectrum-efficient secondary users grouping method according
to claim 8, further comprising the step of adding the MSUs to the
groups of FBSs, the groups of FBS being allowed to use some of the
spectrum allocated to the MSUs.
10. The spectrum-efficient secondary users grouping method
according to claim 9, further comprising the steps of: assigning
the MSUs to suitable groups, the groups being suitable if a
resultant outage probability for both the MSU to be assigned and
the FSUs assigned to the group is less than the target outage
probability threshold; and purchasing a number of channels equal to
the sum of all group categories.
11. The spectrum-efficient secondary users grouping method
according to claim 10, further comprising the step of regrouping an
MSU when an average uplink signal-to-interference-plus-noise ratio
(SINR) of the MSU goes below an MSU SINR threshold level.
12. The spectrum-efficient secondary users grouping method
according to claim 10, further comprising the steps of: the CBS
attempting to find a suitable group for an FSU when the FSU is
moving outside the coverage range of its serving femtocell; and if
no suitable group exists for the FSU, the CBS assigning the FSU to
a new group and purchasing a channel for it.
13. A spectrum-efficient secondary users grouping method for
two-tier cognitive radio networks, comprising the steps of:
grouping femtocell base stations (FBSs) and macrocell secondary
users (MSUs) into non-interfering groups based on a price paid by a
cognitive base station (CBS), the grouping being performed by the
CBS; and serving the FBSs/MSUs within each of the groups using a
common channel.
14. The spectrum-efficient secondary users grouping method
according to claim 13, further comprising the steps of: computing a
utility function to quantify the profit of the CBS, the utility
function including:
.pi..sub.CBS|M.sub.s=.SIGMA..sub.k=1.sup.M.sup.s.eta..sub.ksc.sub.b-1/2w--
c, as a profit of the CBS for one channel, an expression of the
total CBS profit summed over all the groups being:
.pi..sub.CBS.sup.(total)=.SIGMA..sub.s=1.sup.s.SIGMA..sub.k=1.sup.M.sup.s-
(.eta..sub.ksc.sub.b)-1/2wS-cS, where S is a total number of
groups, c.sub.b is the cost paid by a FSU for using the channel, c
s is the price paid by the CBS for the purchased channel, M.sub.s
is the number of FSUs using the channel assigned to Group s, w is
the bandwidth of the channel assigned to Groups s, and .eta..sub.ks
is the spectrum efficiency of the k.sup.th FSU using the channel
assigned to Group s; and re-using the channels based on the
quantified profit of the CBS, whereby an expected sum profit is
maximized on each of the channels.
15. The spectrum-efficient secondary users grouping method
according to claim 13, further comprising the steps of: (a) the CBS
assigning a first FSU to a first group; (b) the CBS finding an
expected profit due to assigning a second FSU to the first group;
(c) the CBS comparing the expected profit to a profit of the first
FSU, the first FSU being the only member in the group; (d) the CBS
assigning the second FSU to the first group if an expected sum
profit is larger than the profit of the first FSU, the CBS setting
said expected profit as an optimum to profit to define a reference
value for subsequent profit comparisons; (e) if the expected sum
profit is smaller than the profit of the first FSU, the CBS
examining subsequent FSUs in the same manner as in steps (b), (c),
and (d) until a last FSU is examined; and (f) repeating steps (a)
through (e) for all ungrouped FSUs until the ungrouped FSUs are
grouped.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to use of orthogonal spectrum
bands in cellular networks, and particularly to a
spectrum-efficient secondary users grouping method for two-tier
cognitive radio networks.
[0003] 2. Description of the Related Art
[0004] The trend in wireless communications industry has been
always towards enhancing spectrum efficiency and energy efficiency
of system operation. The drive for enhancing energy efficiency is
mainly to satisfy the requirements of "green communications" and to
extend the battery lifetime of user equipment (UE). On the other
hand, the need to promote spectrum efficiency of future
communications systems was raised in order to overcome the spectrum
scarcity problem, and at the same time, to allow for increasing
data rate transmission to satisfy the needs of emerging
applications and services
[0005] Cognitive radio (CR) is a self-organized radio that can
sense the spectrum, select the suitable channel to use, transfer
from a spectrum band to another band when necessary, and share the
spectrum with other radios. Cognitive radio was originally proposed
to allow unlicensed secondary users (SUs) to utilize the spectrum
allocated to primary users (PUs) when it is idle. Spectrum trading,
defined as the process of selling and buying spectrum between the
PUs and the SUs, is employed by CR networks to serve their SUs. One
of the major issues in spectrum trading is pricing, which involves
determining the value of the spectrum to the buyer. Since achieving
low spectrum price is crucial to the success of the SU network,
there is a need for a mechanism that helps the SU network to reduce
the amount of spectrum to be purchased from the PU networks.
[0006] Thus, a spectrum-efficient secondary users grouping method
for two-tier cognitive radio networks solving the aforementioned
problems is desired.
SUMMARY OF THE INVENTION
[0007] The spectrum-efficient secondary users grouping method for
two-tier cognitive radio networks groups femtocell base stations
(FBSs) and macrocell secondary users (MSUs) into non-interfering
groups based on their GPS location information, and then serves the
FBSs/MSUs within each group using the same channel.
[0008] A first approach for grouping the secondary users (SUs) is
distance-based. A second approach utilizes profit maximization.
Both approaches are extended to a co-channel deployment scenario
where the FBSs can share part of the channels purchased for the
MSUs to further reduce the number of channels to be purchased from
the PU networks. The distance-based grouping method finds the
minimum number of groups such that the desired quality of service
(QoS) determined by an outage probability threshold is maintained.
The profit maximization method tries to find the set of SUs that
maximizes the expected total profit of the SU network.
[0009] These and other features of the present method will become
readily apparent upon further review of the following specification
and drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is a schematic diagram of a system implementing a
spectrum-efficient secondary users grouping method for two-tier
cognitive radio networks according to the present invention.
[0011] FIG. 2 is a schematic diagram of worst case interference
assumptions solved by a spectrum-efficient secondary users grouping
method for two-tier cognitive radio networks according to the
present invention.
[0012] FIG. 3 is a plot showing average uplink outage probability
resulting from implementing a spectrum-efficient secondary users
grouping method for two-tier cognitive radio networks according to
the present invention.
[0013] FIGS. 4A, 4B, and 4C are plots comparing expected CBS profit
for the cases of no grouping, for an embodiment of a
spectrum-efficient secondary users grouping method for two-tier
cognitive radio networks according to the present invention using
distance-based grouping, and for an embodiment of a
spectrum-efficient secondary users grouping method for two-tier
cognitive radio networks according to the present invention using
profit maximizing based grouping for a sufficient spectrum under
three different assumptions for the path loss exponent n in
Equation (1) (n=3, n=4, and n=5, respectively).
[0014] FIG. 5 is a plot showing average outage probability
resulting from the distance based grouping and the profit
maximizing based grouping embodiments of a spectrum-efficient
secondary users grouping method for two-tier cognitive radio
networks according to the present invention under two different
assumptions for the path loss exponent n in Equation (1) (n=4 and
n=5, respectively).
[0015] FIGS. 6A, 6B, and 6C are plots comparing expected CBS profit
for the cases of no grouping, for an embodiment of a
spectrum-efficient secondary users grouping method for two-tier
cognitive radio networks according to the present invention using
distance-based grouping, and for an embodiment of a
spectrum-efficient secondary users grouping method for two-tier
cognitive radio networks according to the present invention using
profit maximizing based grouping for a limited spectrum under three
different assumptions for the path loss exponent n in Equation (1)
(n=3, n=4, and n=5, respectively).
[0016] FIG. 7 is a plot showing expected CBS profit for the cases
of orthogonal channel deployment and co-channel deployment.
[0017] Similar reference characters denote corresponding features
consistently throughout the attached drawings.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0018] The spectrum-efficient secondary users grouping method for
two-tier cognitive radio networks groups femtocell base stations
(FBSs) and macrocell secondary users (MSUs) into non-interfering
groups based on their GPS location information, and then serves the
FBSs/MSUs within each group using the same channel.
[0019] A first approach for grouping the secondary users (SUs) is
distance-based. A second approach utilizes profit maximization.
Both approaches are extended to a co-channel deployment scenario
where the FBSs can share part of the channels purchased for the
MSUs to further reduce the number of channels to be purchased from
the primary user (PU) networks. The distance-based grouping method
finds the minimum number of groups such that the desired quality of
service (QoS) determined by an outage probability threshold is
maintained. The profit maximization method tries to find the set of
SUs that maximizes the expected total profit of the SU network.
[0020] The present network model 100 is shown in FIG. 1, where L PU
networks (including exemplary networks (110a, 110b, and 110c) offer
part of their spectrum W.sub.i, l=1, . . . , L at a price c.sub.l
per channel to one SU network. The SU network consists of only one
macrocell, so there exists one cognitive base station 102 (CBS) in
the secondary network. The CBS 102 is assumed to be serving I MSUs
104 and K FBSs (including, e.g., FBS 108a, FBS 108b, and FBS 108c)
in the network, and the k.sup.th FBS (where k=1, . . . , K) serves
N.sub.k FSUs 106, which can access the FBS simultaneously. Without
loss of generality, it is assumed that the band offered by each PU
network can be divided into several channels with the same
bandwidth, where each channel satisfies the data rate requirement
of a MSU or a FSU if the signal-to-interference ratio (SIR) is
above a certain threshold. The FBSs are connected to the CBS 102
using broadband connection (e.g., optical fiber or DSL). The
coverage radii of the macrocell and each femtocell are assumed to
be circular, centered at the CBS 102 and the FBS, respectively. All
the femtocells are assumed to have the same coverage radius.
Closed-access is assumed where the femtocell serves only registered
users.
[0021] Each FBS sends its position
{ G k } k = 1 K ##EQU00001##
(determined using a built-in GPS receiver) and the number of users
it serves to the CBS 102 through the wired backhaul. The CBS 102
performs grouping of FBSs and adds MSUs 104 to the groups of FBSs
108a, 108b, 108c based on the location information in order to
satisfy a certain objective. Then, the CBS 102 purchases a number
of channels equal to the number of groups. The offers from each PU
network (110a, 110b, 110c) may differ from time to time, depending
on the PU network load. This requires the PU networks and the SU
network to be perfectly synchronized. The assignment of channels to
different MSUs or FBS groups can be performed by the CBS 102
randomly or according to their spectrum efficiencies to maximize
the CBS profit. The channels purchased from different PU networks
or from the same PU network are assumed to be perfectly
orthogonal.
[0022] Focusing on the uplink signal at an arbitrary BS, it is
assumed that the uplink channels of the desired and the interfering
SUs suffer from path loss and both large-scale (shadowing) and
small-scale (multipath) fading. Under this model, the received
signal power at an arbitrary BS from its served SU can be expressed
as:
P.sub.d.sup.(R)=P.sub.d.sup.(T)r.sub.d.sup.-n.zeta., (1)
where P.sub.d.sup.(T) is the transmit power of the desired SU,
r.sub.d is the distance from the SU to its serving BS, n is the
path loss exponent, and .zeta. is a random variable (r.v.)
modelling the composite fading of the uplink channel experienced by
the desired SU signal. Similarly, the received signal power from
the i.sup.th interfering SU to the desired BS can be expressed
as:
P.sub.i.sup.(R)=P.sub.i.sup.(T)L.sub.ir.sub.i.sup.-n.chi..sub.i,
(2)
where P.sub.i.sup.(T) is the transmit power of the i.sup.th
interfering SU, L.sub.i is the penetration loss due to the
obstacles between the i.sup.th interfering SU and the desired BS,
r.sub.i is the distance between the i.sup.th interfering SU and the
desired BS, and .chi..sub.i is a r.v. modelling the composite
fading of the uplink channel experienced by the i.sup.th
interfering SU signal. Note that SU is used to denote FSUs or MSUs,
and BS is used to denote the FBS for FSUs and the CBS for MSUs.
[0023] Due to the simultaneous effect of both multipath fading and
shadowing, low-mobility users in urban areas experience composite
fading. Composite fading channels have been usually modelled by
log-normal shadowing and Nakagami multipath fading (gamma
distributed power). However, recently, the gamma-gamma (also called
the generalized-K) model has started to gain more attention due to
its tractability and the availability of approximations with high
accuracy. Therefore, it is assumed herein that both the shadowing
and multipath fading effects are modelled using gamma r.v.'s.
Referring to Nakagami's multipath fading model, the instantaneous
received power conditioned on the average local power is modeled as
a gamma r.v. as follows:
p .gamma. ( x ) = 1 .GAMMA. ( m m ) ( m m .OMEGA. ) m m x m m - 1
exp ( - m m .OMEGA. x ) , x > 0 , m m > 0.5 ( 3 )
##EQU00002##
where m.sub.m is the multipath fading parameter that quantifies the
severity of the multipath fading effect (the larger m.sub.m, the
less-severe the multipath fading). The average local power varies
due to the shadowing effect, which is modeled using a gamma r.v.
as:
p .OMEGA. ( y ) = 1 .GAMMA. ( m s ) ( m s .OMEGA. 0 ) m s y m s - 1
exp ( - m s .OMEGA. 0 y ) , y > 0 , m s > 0 ( 4 )
##EQU00003##
where m.sub.s is the shadowing parameter that quantifies the
severity of the shadowing effect (the larger m.sub.s, the
less-severe the shadowing), and .OMEGA..sub.0 is the mean of the
average local power received at the desired BS. The transmit power,
the penetration loss, and the path loss can be incorporated in the
average of the received mean local power of the desired user
(.OMEGA..sub.0d) and the i.sup.th interfering user (.OMEGA..sub.0i)
as:
.OMEGA..sub.0d=P.sub.d.sup.(TX)r.sub.d.sup.-n, and
.OMEGA..sub.0i=P.sub.i.sup.(TX)L.sub.ir.sub.i.sup.-n. (5)
[0024] The resulting gamma-gamma (generalized-K) distribution of
composite fading can be approximated (through matching the first
two moments of the gamma-gamma distribution) by a gamma
distribution with the following parameters:
.kappa. = m m m s m m + m s + 1 - m m m s .epsilon. , .theta. =
.OMEGA. .kappa. , ( 6 ) ##EQU00004##
where .kappa. and .theta. are the scale and the shape parameters of
the approximate composite fading r.v., respectively, and .epsilon.
is the adjustment factor.
[0025] In order to reduce the number of channels to be purchased
from the PU networks, the CBS needs to group the FBSs into
non-interfering groups based on the distances between them.
Grouping the FBSs into non-interfering groups requires that the
distance from a FSU to a FBS in another femtocell should be found
in order to determine whether the FSU is interfering with that
femtocell or not. However, since the coverage radius of a femtocell
is usually very small (from 10 to 30 meters), the distance from a
FSU to a FBS in another femtocell can be well approximated by the
distance between the two FBSs. In the following, the distance-based
grouping approach is illustrated, and its complexity and the uplink
outage probability are analyzed. Next, the distance threshold
minimization is implemented based on the worst-case interference
assumptions. Finally, the scheme is extended to the co-channel
deployment scenario by adding the MSUs to the groups of FBSs.
[0026] The distance-based grouping scheme can be implemented as
follows. At first, each FBS determines its location using its GPS
and sends it to the CBS. The CBS finds the distances between the
femtocells and stores them. Starting with the first FBS (assuming
that the CBS assigns an index for each FBS to distinguish it from
the other FBSs, so the first FBS is the one with the smallest
index), the CBS assigns that FBS to the first group, and it stores
the number of FSUs served by that FBS as the category of the group.
The category of the group here is defined as the maximum allowed
number of FSUs per one FBS member, which corresponds to the number
of channels needed to be assigned to that group. The second FBS is
then examined by the CBS, and if the distance between the second
and the first FBSs is larger than a distance threshold D.sub.th and
the number of FSUs served by the second FBS is less than or equal
to the category of the group, then the CBS assigns the second FBS
to the first group. Otherwise, if any of the previously described
conditions is not satisfied, then the second FBS is not grouped,
and the CBS examines the third FBS and so on. When all the FBSs are
examined, the CBS restarts from the first ungrouped FBS and assigns
it to the second group. Each time, the CBS checks all the ungrouped
FBSs to examine whether they can be assigned to a certain group or
not. This process is repeated until all the FBSs are grouped, where
a FBS is assigned to a group if its distance to all the members of
that group is larger than D.sub.th and the number of FSUs it serves
is less than or equal to the category of the group.
[0027] If a new FSU appears in one of the existing femtocells, its
FBS reports to the CBS that it has a new FSU. The CBS checks
whether the FBS still satisfies the category condition, and if not,
then the CBS increases the category of the group by one and
purchases a new channel for it. Further, if a new FBS with an
arbitrary number of FSUs appears in the network, it sends its
location and the number of its FSUs to the CBS, which, in turn,
groups the new FBS according to the algorithm described above.
[0028] It is important to point out that grouping the FBSs is one
approach to implementing the distance-based grouping scheme.
Another way to perform distance-based grouping is to group the FSUs
based on the distances between them. However, when the number of
FSUs in the network is large, which is expected in dense FBS
deployment environments, the complexity of FSU grouping becomes
significantly high. Thus, grouping the FBSs serves as a
less-complex implementation of the distance-based grouping scheme,
since the number of FBSs is usually much smaller than the number of
FSUs with very similar performance. The first step in the
distance-based grouping scheme is to assign the first ungrouped FBS
to a group, and all the other ungrouped FBSs are examined by the
CBS to check whether they can be assigned to the group or not. If a
FBS is assigned to a group (i.e., it satisfies the distance
threshold and the category conditions), it will not be examined for
the subsequent groups. The worst-case complexity occurs when each
FBS is assigned to a separate group. In this case, each FBS is
examined with all the FBSs with an index higher than its index.
Assuming that K FBSs exist in the network, then the CBS needs, at
most, K-1 operations for the first group, K-2 operations for the
second group, and so on. An operation here is defined as the
processes required to examine whether a FBS can be assigned to a
certain group or not. This includes finding the distance between
this FBS and all FBSs assigned to the group, comparing this
distance to D.sub.th, comparing the number of FSUs served by the
FBS with the category of the group, and all the accompanying
assignment and counting operations. For K FBSs, the CBS needs, at
most:
i = 1 K ( K - i ) = 1 2 K ( K - 1 ) ##EQU00005##
operations. So, the complexity of the distance-based grouping
scheme is on the order of O(K.sup.2).
[0029] The complexity of the update process is defined as the
average number of groups to be examined before finding a suitable
group for the new FBS (denoted as the (K+1).sup.th FBS), given that
S groups have been already formed by the grouping scheme with
M.sub.s (s=1, . . . , S) FBS members per each group. The new FBS
will be assigned to Group s if it satisfies the distance threshold
condition:
{ D ( K + 1 ) j } j = 1 M S .gtoreq. D th , ##EQU00006##
where D(K+1)j is the distance from the (K+1).sup.th FBS to the
j.sup.th FBS member in Group s, and the category condition
N.sub.k.ltoreq.C.sub.s. The category of each group (C) is
determined by the number of FSUs in the first femtocell member of
that group.
[0030] To find the average number of groups to be examined before a
suitable group is found, let z=1, . . . , S be a r.v. representing
the number of groups to be examined before finding the group that
satisfies the distance threshold condition:
( { D ( K + 1 ) j } j = 1 M S .gtoreq. D th ) ##EQU00007##
and the category condition N.sub.K+1.ltoreq.C.sub.s. The
probability that one group is examined is the probability that the
first group satisfies the two conditions:
(i.e.,
Pr{z=1}=.pi..sub.i=1.sup.M.sup.1P.sub.r{D.sub.i(K+1).gtoreq.D.sub-
.th}.times.Pr{N.sub.(K+1).ltoreq.C.sub.1}).
[0031] In the same way, the probability that two groups are
examined is the probability that the first group fails to satisfy
the condition and the second group satisfies it, i.e.,:
Pr{z=2}=[1-(.pi..sub.i=1.sup.M.sup.1Pr{D.sub.i(K+1).gtoreq.D.sub.th})Pr{-
N.sub.(K+1).ltoreq.C.sub.1}](.pi..sub.i=1.sup.M.sup.2Pr{D.sub.i(K+1).gtore-
q.D.sub.th}).times.Pr{N.sub.(K+1).ltoreq.C.sub.2}) (7)
[0032] Generally, the probability that s groups are examined can be
written as:
Pr { z = s } = i = 1 s - 1 [ 1 - ( .PI. j = 1 M i Pr { D j ( K + 1
) .gtoreq. D th } ) Pr { N ( K + 1 ) .ltoreq. C i } ] ( .PI. v = 1
M s Pr { D v ( K + 1 ) .gtoreq. D th } ) Pr { N ( K + 1 ) .ltoreq.
C s } ) ( 8 ) ##EQU00008##
Note that the event {z=S} may occur in two cases. The first case is
when the last group satisfies the condition, and the second case is
when no group can satisfy the condition (i.e., when the FBS is
assigned to a new group). Based on the aforementioned discussion,
the average number of examined groups before a suitable group is
found (z) can be written as:
z _ = s = 1 S s i = 1 s - 1 [ 1 - .PI. j = 1 M i [ Pr { D j ( K + 1
) .gtoreq. D th } Pr { N ( K + 1 ) .ltoreq. C i } ] ] .PI. v = 1 M
s [ Pr { D v ( K + 1 ) .gtoreq. D th } Pr { N ( K + 1 ) .ltoreq. C
s } ] + S a = 1 S [ 1 - .PI. n = 1 M a [ Pr { D n ( K + 1 )
.gtoreq. D th } Pr { N ( K + 1 ) .ltoreq. C n } ] ] . ( 9 )
##EQU00009##
[0033] The expression in (9) depends on the probability that the
distance between two FBSs is larger than D.sub.th. When the FBSs
are distributed using Poisson point process (PPP), their locations
will be uniformly and independently distributed in the macrocell
region. In this case, the probability that the distance between two
FBSs inside the circular range of the macrocell (with radius
R.sub.M) is smaller than D.sub.th can be written as:
Pr { D .ltoreq. D th } = 1 + 2 .pi. ( D th 2 R M 2 - 1 ) cos - 1 (
D th 2 R M ) - D th .pi. R M ( 1 + D th 2 2 R M 2 ) 1 - D th 2 4 R
M 2 ( 10 ) ##EQU00010##
Hence, the probability that two FBSs are at a distance of at least
D.sub.th is just the complement of the probability in (10).
However, given that the coverage radii of two femtocells do not
overlap with each other (this condition is put to ensure that a FSU
served by a FBS is not in the range of another FBS belonging to the
same group to avoid severe interference among group members); that
is, the distance between two FBSs should be greater than or equal
to double the radius of the FBS (denoted by R.sub.F), the
probability that two FBSs inside the circular range of the
macrocell are at a distance of at least D.sub.th can be expressed
as:
Pr { D .gtoreq. D th | D .gtoreq. 2 R F } = Pr { D .gtoreq. D th ,
D .gtoreq. 2 R F } Pr { D .gtoreq. 2 R F } = Pr { D .gtoreq. D th }
Pr { D .gtoreq. 2 R F } = D th .pi. R M ( 1 + D th 2 2 R M 2 ) 1 -
D th 2 4 R M 2 - 2 .pi. ( D th 2 R M 2 - 1 ) cos - 1 ( D th 2 R M )
2 R F .pi. R M ( 1 + 2 R F 2 R M 2 ) 1 - R F 2 R M 2 - 2 .pi. ( 4 R
F 2 R M 2 - 1 ) cos - 1 ( R F R M ) . ( 11 ) ##EQU00011##
[0034] In addition to the distance distribution, a model is needed
for the number of FSUs per femtocell. Assuming that the number of
FSUs in a femtocell can be modeled as a Poisson r.v. with parameter
.lamda. representing the average number of FSUs per femtocell, the
probability that the number of FSUs in a femtocell is smaller than
or equal to some value is just the cumulative distribution function
(cdf) of the Poisson r.v., which can be approximated using the cdf
of the non-central Chi-square (.chi..sup.2) r.v. (with a
non-centrality parameter of 2.lamda. and 2(m+1) degrees of freedom)
as follows:
Pr{N.ltoreq.m}=1-F.sub..chi..sup.2(2.lamda., 2(m+1)), m is integer
(12)
However, since there is a maximum number of users (N.sub.max) that
can be served by a FBS, which depends on the architecture of the
FBS itself, equation (12) should be modified to consider this
condition as follows:
Pr { N .ltoreq. m | N .gtoreq. N max } = Pr { N .ltoreq. m } Pr { N
.ltoreq. N max } = 1 - F .chi. 2 ( 2 .lamda. , 2 ( m + 1 ) ) 1 - F
.chi. 2 ( 2 .lamda. , 2 ( N max + 1 ) ) , m is integer ( 13 )
##EQU00012##
[0035] Since the expressions in (11) and (13) do not depend on the
location of the FBS and its number of served FSUs, the expression
in (9) simplifies as:
z _ = s = 1 S s i = 1 s - 1 ( 1 - [ Pr { D .gtoreq. D th | D
.gtoreq. 2 R F } Pr { Pr { N .ltoreq. C s | N .ltoreq. N max } ] M
i ) .times. [ Pr { D .gtoreq. D th | D .gtoreq. 2 R F } Pr { N
.ltoreq. C s | N .ltoreq. N max } ] M s + S a = 1 S ( 1 - [ Pr { D
.gtoreq. D th | D .gtoreq. 2 R F } Pr { N .ltoreq. C s | N .ltoreq.
N max } ] M a ) ( 14 ) ##EQU00013##
[0036] After assigning the k.sup.th FBS to Group s, one of the
channels reserved for this group is utilized by one of the FSUs
served by that FBS. Therefore, the outage event at the FBS can be
defined as the probability that the uplink signal-to-interference
ratio (SIR) at the FBS from the desired FSU using one of the
channels assigned to Group s will fall below a certain threshold,
given that S groups have been formed by the grouping scheme, with
M.sub.s members in Group s, s=1, . . . , S. Therefore, in order to
find the outage probability, the probability that a FSU is
utilizing the channel of Group s should be found. The probability
that the FSU served by the k.sup.th FBS is utilizing an uplink
channel belonging to Group s is the probability that this FBS
satisfies the distance threshold condition:
( { D ( K + 1 ) j } j = 1 M s .gtoreq. D th ) ##EQU00014##
and the category condition N.sub.K.ltoreq.C.sub.s, where C.sub.s is
the category of Group s).
[0037] The probability that the k.sup.th FBS is assigned to the
first group is the probability that the first group satisfies the
two conditions i.e.,:
Pr{s=1}=p.sub.k1=.pi..sub.i=1.sup.M.sup.1P.sub.r{D.sub.ik.gtoreq.D.sub.t-
h}.times.Pr{N.sub.K.ltoreq.C.sub.1}.
In a similar way, the probability that the k.sup.th FBS is assigned
to the second group is the probability that the first group does
not satisfy the two conditions and the second group does so,
i.e.,:
Pr { s = 2 } = p k 2 = [ ( 1 - i = 1 M 1 P r { D ik .gtoreq. D th }
) Pr { N K .ltoreq. C 1 } ] ( i = 1 M 2 P r { D ik .gtoreq. D th }
) .times. Pr { N K .ltoreq. C 2 } . ( 15 ) ##EQU00015##
[0038] The expression of the uplink outage probability averaged
over all the possible groups to which the FBS is likely to be
assigned can be generalized as:
P out ( k ) = s = 1 S [ P out | s ( k ) .times. p ks ] = s = 1 S s
i = 1 s - 1 [ 1 - ( Pr { D .gtoreq. D th } ) M i Pr { N k .ltoreq.
C i } ] .times. ( Pr { D .gtoreq. D th } ) M s Pr { N k .ltoreq. C
s } .times. P out | s ( k ) , ( 16 ) ##EQU00016##
where, p.sub.ks is the probability that the k.sup.th FBS is
assigned to Group s, and P.sub.out|s.sup.(k) is the outage
probability, given that the FSU under consideration is utilizing
the channel assigned to Group s (depends on the number of the
members of Group s, and on their distances from the k.sup.th FBS).
Hence:
P out | s ( k ) = Pr { P k i .di-elect cons. V s i .noteq. k P i
< a } , ( 17 ) ##EQU00017##
where P.sub.k and P.sub.i are the received powers from the desired
FSU and the i.sup.th interfering FSU at the k.sup.th desired FBS,
respectively, a is the SIR threshold, and V.sub.s is a vector
containing the indices of the FBS members of Group s, which
correspond to the indices of the interferers, since only one FSU
from each femtocell interferes with the FSUs in the other
femtocells belonging to the same group.
[0039] To find P.sub.out|s, the following worst-case interference
assumptions are used to simplify the outage probability expression.
An illustration of the worst-case interference assumptions is shown
in FIG. 2. First, it is assumed that the FSU 210 served by the
desired FBS 208 (in the central femtocell) and all the FSUs served
by other FBSs 208 (in the surrounding femtocells 216a, 216b, 216d)
belonging to the same group are transmitting at the same time.
Second, the interfering FSUs 212 exist at the edge of their
respective femtocells towards the desired FBS 208 (central
femtocell 216c), and the desired FSU 210 is at the edge of its
femtocell (central femtocell 216c). When uplink power control is
assumed, placing the FSUs at the edge of their respective
femtocells implies that they are using the maximum allowed power to
transmit.
[0040] Since a gamma distribution is assumed to model composite
fading for both the desired and interfering FSUs, it is needed to
find the distribution of the ratio of a gamma r.v. to the sum of
independent non-identically distributed (i.n.d.) gamma r.v.'s. A
derivation of an approximation for the distribution of the ratio of
a gamma r.v. to the sum of i.n.d. gamma r.v.'s results in the
outage probability as follows:
P out | s = .GAMMA. ( .kappa. d + .kappa. e ) .GAMMA. ( .kappa. d )
.GAMMA. ( .kappa. e ) ( .OMEGA. 0 e .OMEGA. 0 d ) .kappa. d a
.kappa. d F 1 2 ( ( .kappa. d ) , .kappa. d + .kappa. e , 1 +
.kappa. d , - a ( .OMEGA. 0 e .OMEGA. 0 d ) ) .kappa. d , ( 18 )
##EQU00018##
where .sub.2F.sub.1(.) denotes the hypergeometric function, k.sub.d
is the shape parameter of the desired FSUs composite fading
channel, k.sub.e and .OMEGA..sub.0e are the shape parameter and the
average power of the approximate distribution for the sum of i.n.d.
gamma r.v.'s given as:
.OMEGA. 0 e = i .di-elect cons. V s i .noteq. k .OMEGA. 0 i ,
.kappa. e ( i .di-elect cons. V s i .noteq. k .OMEGA. 0 i ) 2 i
.di-elect cons. V s i .noteq. k .OMEGA. 0 i 2 .kappa. i . ( 19 )
##EQU00019##
where k.sub.i and .OMEGA..sub.0i are the shape parameter and the
average power of the interfering FSUs composite fading channel.
Since the distances from the desired FBS to the desired interfering
FSUs are incorporated in the mean of the received power, the outage
expression is conditioned on the number of members in Group s and
their distances from the desired FBS.
[0041] It can be directly seen that the smaller the D.sub.th used
to group the FBSs, the smaller the number of formed groups. This is
because as D.sub.th becomes smaller, satisfying the distance
threshold condition becomes more probable. Since the objective of
the CBS is to minimize the number of groups (corresponding the
number of channels to be purchased), it follows that the CBS should
use the minimum possible D.sub.th that satisfies the target
QoS.
[0042] The uplink outage probability is a monotonically decreasing
function of D.sub.th. The decrease of the uplink outage probability
with the increase of D.sub.th can be intuitively justified as
follows. With the increase of D.sub.th, the probability that two
FBSs are separated by a distance larger than D.sub.th becomes
lower. Therefore, the number of FBSs per group is expected to
decrease with the increase of D.sub.th. A smaller number of FBSs
per group implies a smaller number of interferers on each channel,
which, on average, corresponds to a smaller outage probability.
Based on this intuition, and assuming that the CBS has some target
outage probability to achieve given the desired
signal-to-interference ratio (SIR), the present method can make use
of the bisection method to find the minimum D.sub.th for each group
of FBSs as follows.
[0043] For the first group, the CBS starts with D.sub.th=2R.sub.F
and forms the group. Then, based on the distances between the FBSs,
the CBS finds the expected uplink outage probability at each FBS
assigned to the group using equation (14). The CBS compares the
maximum uplink outage probability with the target one, and if it is
smaller, the CBS chooses R.sub.F as D.sub.th. Otherwise, the CBS
increments the value of D.sub.th and performs grouping until the
maximum uplink outage probability becomes lower than the target
one. The CBS fixes the last two values of D.sub.th as the desired
range. Finally, the CBS applies the bisection method on the desired
range to find the optimum value of D.sub.th for that group. Once
the first group is optimized, this process is repeated again to
build the second group, and sequentially until all FBSs are
grouped. It should be noticed here that different values of
D.sub.th may be chosen for different groups.
[0044] To further reduce the number of channels to be purchased by
the CBS from the PU networks, the groups of FBSs should be allowed
to use some of the spectrum allocated to the MSUs. This can be
achieved by adding the MSUs to the groups of FBSs. To maintain the
QoS of both the MSUs and the FSUs, the CBS should ensure that
adding a MSU to a FBS group does not result in an average uplink
outage probability for both the FSUs and the MSU that is larger
than the outage probability threshold. It should be emphasized here
that assigning a MSU to a group means that the channel allocated to
that MSU can be shared by all the FBS members of the group
(assigned to one FSU per FBS member).
[0045] Conventional uplink power control is assumed to be utilized
by the MSUs, where the MSU transmits either at a power level enough
to compensate for the channel between the MSU and the CBS, or at
the maximum allowed power level if it cannot compensate for the
channel. That is, the transmit power of the MSU is written as:
P.sub.t=min(P.sub.max, P.sub.0/.gamma.), (20)
where P.sub.max is the maximum allowed power for the MSUs, P.sub.0
is a design parameter used to set some desired SIR at the base
station, and .gamma. is the composite fading channel gain modeled
as in equation (3).
[0046] The scheme is initialized with the groups formed using the
distance-based grouping scheme. Then the CBS starts with the first
MSU, and it searches for a suitable group and assigns the MSU to
that group. A group is considered suitable for a MSU if the
resultant outage probability for both the MSU and the FSUs assigned
to the group, assuming they are transmitting simultaneously, is
less than the target outage probability threshold. A MSU that
cannot be assigned to any of the FBS groups is assigned to a
separate group with a category equal to one. After grouping the
MSUs, the CBS purchases a number of channels equal to the sum of
all group categories.
[0047] Due to their movements, the MSUs need to be re-grouped by
the CBS in order to maintain their QoS. Since the uplink signal is
considered, the CBS can find the average uplink SINR of the MSUs by
observing the uplink signal received from each MSU over some
observation window. The process of re-grouping a MSU is triggered
when the average uplink SINR of that MSU goes below some (MSU SINR)
threshold level. The MSU is re-grouped using a co-channel
deployment extension.
[0048] Another case of interest is when a FSU is moving outside the
coverage range of its serving femtocell. In this case, the FSU
requests service from the CBS as a part of the handover operation,
and the CBS tries to find a suitable group for this FSU if any.
Otherwise, if no suitable group exists for the FSU, the CBS assigns
the FSU to a new group and purchases a channel for it.
[0049] The aforementioned strategy was to minimize the number of
purchased channels while maintaining a target outage probability.
This can serve the situation when the QoS is guaranteed. However,
it is not necessary that this strategy will maximize the CBS
profit. This is because minimizing the number of purchased channels
is achieved by assigning a larger number of FSUs to each group.
This will result in a smaller value of the expected SIR for each
FSU due to the strong interference, resulting in a lower expected
sum rate (profit) for the CBS, where it is assumed that the CBS
profit is directly proportional to the sum rate of the FSUs and
MSUs. Table 1 presents pseudocode for the distance based
grouping.
TABLE-US-00001 TABLE 1 Pseudocode for the Distance Based Grouping
Step Number Function 1 Initialization: the set of FBSs
.OMEGA..sub.K = {1, 2, ..., K }.sub.K, the set of FBSs locations
{G.sub.k }.sub.k=1, and the set of grouping indices G = g.sub.1,
g.sub.2, ..., g.sub.K . Each FBS serves N.sub.k users. The category
of each Group s is C.sub.s which is set to 0 for all groups 2 Set s
= 1. 3 repeat 4 Denote the number of FBSs in Group s by M.sub.s ,
and set M.sub.s to zero. 5 Find the first FBS (with index k) with
grouping index g.sub.k = 0, and assign it to Group s. 6 : Set n = k
+ 1, M.sub.s = M.sub.s + 1, and C.sub.s = N.sub.k . 7 repeat 8 if
g.sub.n == 0 then 9 Find the distance between the n.sup.th FBS and
all the FBSs in Group s, {D.sub.ni}.sup.M.sub.s ; 10 if {Dni }Ms
.gtoreq. Dth then 11 if N .ltoreq. C.sub.s then 12 Assign FBS n to
Group s, 13 Set M.sub.s = M.sub.s + 1, and g.sub.n = 1 14 end if 15
end if 16 end if 17 Set n = n + 1. 18 until n = K + 1, end repeat.
19 Set s = s + 1. 20 until all elements in G equal 1, end repeat.
21 Output the number of groups, and the members of each group.
[0050] The profit-maximizing grouping approach is first presented
for the orthogonal channel deployment case, where the channels
allocated for the FBSs are orthogonal to those allocated for the
MSUs. Then, the scheme is extended to the co-channel deployment
scenario by adding the MSUs to the groups of FSUs. To maximize the
total profit of the SU network, the CBS needs to group the FBSs and
re-use the channels such that the expected sum profit is maximized
on each channel. We utilize the quadratic utility function to
quantify the profit of the CBS, but with simplifications. For
example, the CBS cannot switch among the channels offered by
different PU networks. This assumption is used to simplify the
utility function by excluding the term that corresponds to risk
aversion (by setting the substitutability parameter to zero.sup.5),
since the focus here is on the spectrum allocation problem. It is
assumed here that the spectrum offered by different PU networks has
the same price per channel (assuming that a collusion with price
fixing is established and maintained by the PU networks). Each
purchased channel may be utilized by several FSUs simultaneously.
Based on these simplifications, the profit of the CBS on the
channel assigned to Group s, can be characterized by the
relation:
.PI. CBS | M s = k = 1 M s w .eta. ka c b - 1 2 w 2 - cw , ( 21 )
##EQU00020##
where w is the bandwidth of the channel assigned to Groups s
(assumed to be fixed for all groups), c.sub.b is the cost paid by a
FSU for using the channel, c is the price paid by the CBS for the
purchased channel, and M.sub.s is the number of FSUs using the
channel assigned to Group s, and .eta..sub.ks is the spectrum
efficiency of the k.sup.th FSU using the channel assigned to Group
s. When adaptive modulation is utilized, the spectrum efficiency of
MSU/FSU transmission can be obtained as:
.eta. ks = log 2 ( 1 + J .gamma. ks ) , where J = 1.5 ln ( 0.2 /
BER ( t ) ) , ( 22 ) ##EQU00021##
where .gamma..sub.ks is the uplink SINR at the k.sup.th FBS when
its FSU is utilizing the channel assigned to Group s, and
BER.sup.(t) is the target bit error rate (BER). Since the bandwidth
w is a common factor in equation (21), a normalized version of (21)
can be written as:
.pi..sub.CBS|M.sub.s=.SIGMA..sub.k=1.sup.M.sup.s.eta..sub.ksc.sub.b-1/2w-
-c. (23)
Hence, the total CBS profit, summed over all the groups, can be
expressed as:
.pi..sub.CBS.sup.(total)=.SIGMA..sub.s=1.sup.s.SIGMA..sub.k=1.sup.M.sup.-
s(.eta..sub.ksc.sub.b)-1/2wS-cS. (24)
where S is the total number of groups.
[0051] The utility function in equation (23) represents the profit
of the CBS from one channel. It can be seen from equation (23) that
allocating a channel to a small number of FSUs would increase the
spectrum efficiency for those FSUs (due to the absence of
interference), and hence would increase the CBS revenue from that
channel, but more channels should be purchased. On the other hand,
if the CBS allocates the channel to many FSUs, the number of
purchased channels is reduced, but the revenue gained from each
user is lower due to interference, which affects the spectrum
efficiency of user transmission. Therefore, the problem that needs
to be solved here is to determine how many groups should be formed
and how many FSUs should be assigned to each group such that the
CBS total expected profit is maximized on the channel allocated to
each group, which will result in maximizing the total CBS profit
over all the channels. The direct way to solve such a problem is by
performing an exhaustive search over all the possible set of FSUs
for each group and choosing the set that results in the maximum
expected profit for the CBS. However, the complexity of this
solution is O(N!), where N is the total number of FSUs in the SU
network. For a large number of FSUs, such a solution will be
time-consuming, since the complexity of the algorithm increases
factorially with the number of FSUs. Instead, we propose the use of
the greedy approach, which is a very well-known approach in the
context of optimization and resource allocation in femtocell
networks to reduce the complexity of the algorithm to O(N.sup.2),
which is a polynomial-time complexity.
[0052] The present greedy algorithm for profit maximization is
implemented as follows. The CBS starts with the first FSU and
assigns it to the first group. Then, the CBS finds the expected
profit due to assigning the second FSU to the first group and
compares it to the profit of the first FSU being the only member in
the group. If the first profit is larger, the CBS assigns the
second FSU to the first group, and sets its expected profit as the
optimum profit, which will be the reference value for the
subsequent comparisons. Otherwise, the CBS examines the third FSU
and so on, until the last FSU is examined. The process is repeated
until all the FSUs are grouped, where a FSU is assigned to a group
if the following condition is satisfied:
.PI. _ CBS | M s = k = 1 M s .eta. ks c b - 1 2 w - c . ( 25 )
##EQU00022##
where .pi..sub.CBS|M is the expected sum profit of the CBS from
assigning M FSUs to the group, and:
.pi..sub.CBS|M-1.sup.(max)
is the maximum expected sum profit, given that M-1 FSUs have been
already assigned to the group. It is important to point out here
that the greedy algorithm does not usually find the global optimal
point, but in many cases, it ends up finding a local optimum,
rather than getting the global one. A better suboptimal solution
can be found by using the N-path greedy solution, where for each
group, the CBS finds the optimum set of members starting from each
ungrouped FSU. Then it chooses the set that achieves the maximum
expected profit. However, this enhancement in profit is attained at
the cost of more processing time because the complexity of the
N-path solution is O(N.sup.3), since it is just the greedy
algorithm repeated N times (for each FSU).
[0053] The problem in finding the spectrum efficiency in (19) is
that since the CBS still does not have the channels, the SIR cannot
be measured before the channel is purchased from the PU network. To
overcome this problem, the CBS should try to estimate the SIR under
the worst-case scenario described in the previous section. Under
composite fading scenario and considering the worst-case
interference conditions, the pdf of the SIR is just the pdf of the
ratio of a gamma r.v. to the sum of i.n.d. gamma r.v.'s, which can
be obtained using a derived approximation and the expected SIR for
the approximated pdf is written as:
E { SIR } = .OMEGA. 0 d .OMEGA. 0 e .kappa. e .kappa. e - 1 ,
.kappa. e > 1 , ( 26 ) ##EQU00023##
where .OMEGA..sub.0e and k.sub.e are defined as in equation (19).
Table 2 presents pseudocode for the profit maximizing based
grouping.
TABLE-US-00002 TABLE 2 Pseudocode for the Profit Maximizing Based
Grouping Step Number Function 1 Initialization: the set of FBSs
.OMEGA..sub.K = {1, 2, ..., K }.sub.K, the set of FBSs locations
{G.sub.k }.sub.k=1 , and the set of grouping indices G = g.sub.1,
g.sub.2, ..., g.sub.K . . Each FBS serves N.sub.k ungrouped users.
2 Set s = 1. 3 repeat 4 Denote the number of FSUs in Group s by
M.sub.s , and set M.sub.s to zero. 5 Find the first FBS k with
grouping index g.sub.k = 0, and assign it to Group s. 6 Set n = k +
1, M.sub.s = M.sub.s + 1, and N.sub.k = N.sub.k - 1. 7 Set
.PI.(max) == .PI.C BS N I . C BS 8 if N.sub.k == 0 then 9 Set
g.sub.k = 0; 10 end if. 11 repeat 12 if g.sub.n == 0 then 13 Find
the distance between the FBS n and all the FBSs in Group s,
{D.sub.ni }.sub.i=1; 14 Find the expected profit of the CBS from
assigning the FSU served by the FBS n to Group s, .PI..sub.C B
S|M.sub.s.sub.+1 . 15 if .PI..sub.C B S|M.sub.s.sub.+1 >
.PI..sub.C BS then 16 Assign FBS n to group s, 17 Set M.sub.s =
M.sub.s + 1 , N.sub.n = N.sub.n - 1 , and ) .PI..sub.C B
S.sup.(max) = .PI..sub.C B S |M.sub.s.sub.+ 1 . 18 if N.sub.n == 0
then 19 Set g.sub.n = 1; 20 end if; 21 end if. 22 end if. 23 Set n
= n + 1. 24 until n = K + 1, end repeat. 25 Set s = s + 1. 26 until
all elements in G equal 1, end repeat. 27 Output the number of
groups, and the members of each group.
[0054] To examine the performance of the scheme under spectrum
insufficiency scenarios, a modified version of equation (24) is
considered by assuming that the CBS profit will saturate when the
number of groups reaches the number of channels offered by the PU
networks. Therefore, assuming that the total number of channels
offered by the PU networks is fixed at B, the expected total CBS
profit can be written as:
.PI. _ CBS ( total ) = { s = 1 S k = 1 M s .eta. ks c b - 1 2 wS -
cS , S .ltoreq. B ; s = 1 B k = 1 M s .eta. ks c b - 1 2 wB - cB ,
S > B . ( 27 ) ##EQU00024##
When the number of offered channels is insufficient to serve all
the groups, the CBS sorts the groups in a descending order
according to the sum of spectrum efficiencies of the members of
each group and allocates the channels to the first B groups to
maximize its profit.
[0055] Similar to the distance-based co-channel deployment
extension described in above, some of the MSUs can be added to the
groups of FSUs, which have been formed using the profit
maximization grouping scheme described herein. However, the
condition that needs to be satisfied does not depend on the QoS or
the outage probability. For each MSU and each group of FSUs, the
CBS has two choices: either to purchase two orthogonal channels for
the MSU and the group of FSUs, or to add the MSU to the group of
FSUs and purchase only one channel. The CBS will add the MSU to the
group of FSUs only if sharing the channel will result in a higher
expected profit for the CBS than when the MSU is assigned an
orthogonal channel. Therefore, the condition to be satisfied in
order to assign a MSU to a group of FSUs is:
.pi..sub.Co.gtoreq..pi..sub.NI, (28)
where .pi..sub.Co is the expected sum profit when one channel is
purchased and shared among the MSU and the group of FSUs, and
.pi..sub.NI is the expected sum profit when two orthogonal channels
are purchased (i.e., when there is no interference between the MSU
and the group of FSUs). An MSU that is not added to a group of FSUs
is assigned to a separate group. After adding some of the MSUs to
the groups of FSUs, the CBS purchases the number of channels enough
to serve the groups if the offered spectrum is sufficient. If the
spectrum is insufficient for serving the groups, then the CBS sorts
the groups according to the sum of spectrum efficiencies of their
members and assigns the channels to the groups with the highest
sums to maximize its profit.
[0056] In the simulation described below, the coverage radii of the
macrocell and each femtocell are assumed to be 100 m and 20 m,
respectively. The other parameters will be mentioned independently
for each part. The performance of the distance-based grouping
scheme, in terms of the average resulting number of channels to be
purchased from the PU networks and the average resultant outage
probability, is compared for the cases of no grouping, grouping
with orthogonal channel deployment, and grouping with co-channel
deployment. The FBSs and the MSUs are distributed using PPP with an
average number defined as the network density, and the number of
FSUs per femtocell follows a Poisson distribution with parameter
.lamda.=2 FSUs per femtocell and maximum number of four FSUs per
femtocell. The FBSs constitute 40% of the total number of MSUs and
FBSs in the network. The SIR threshold is fixed at 10 dB, the
outage threshold is fixed at 10.sup.-3, and the penetration loss is
assumed to be 15 dB. The channels from an interfering FSU to FBS,
desired FSU to FBS, interfering FSU to CBS, and MSU to CBS are
modeled using a gamma r.v. with shadowing and fading parameters
(m.sub.s, m.sub.m)=[(1, 1), (4.23, 4), (1, 1), (2.5, 4)] (shadowing
parameter m.sub.s=1, 2.5, 4.23 correspond to shadow spread
.sigma..sub.s=7, 5, 4 dB).
[0057] Table 3 shows the average number of channels to be purchased
versus the network density for the cases of no grouping, grouping
with orthogonal channel deployment, and grouping with co-channel
deployment under several interference conditions characterized by
the value of the path loss exponent n (the larger is n, the less
severe is the interference). The first observation here is the
significant reduction in the number of channels to be purchased
from the PU networks as a result of applying the grouping scheme
when compared to the case of no grouping. The second observation is
that the (optimized) grouping scheme can exploit the less severe
interference conditions to further reduce the number of groups by
grouping at a smaller value of D.sub.th. The third observation is
the reduction in the number of channels to be purchased as a result
of applying the co-channel deployment extension, which improves the
spectrum efficiency of the scheme. The reduction in the number of
channels to be purchased resulting from the co-channel deployment
extension is at the cost of worse outage performance for both the
FSUs and MSUs. The average MSUs and FSUs uplink outage
probabilities versus the network density are shown in plot 300 of
FIG. 3 for different values of n. As it can be noticed from plot
300, the scheme with co-channel deployment compromises the QoS of
the FSUs and the MSUs to further reduce the number of purchased
channels. Since the outdoor environment is usually more severe than
the indoor one, which shows in the MSUs uplink outage probability
as compared to the FSUs uplink outage probability, the use of the
co-channel deployment extension is limited with the QoS
requirements of the MSUs.
TABLE-US-00003 TABLE 3 The Average Number of Channels to be
Purchased from the PU Networks Network density (per meter square)
0.005 0.015 0.025 0.035 0.045 No grouping 219 659 1099 1538 1978
Grouping, Orthogonal, n = 3 114 341 550 793 1016 Grouping, Co-Chan,
n = 3 112 338 546 788 1012 Grouping, Orthogonal, n = 4 113 325 551
754 973 Grouping, Co-Chan, n = 4 110 322 547 749 967 Grouping,
Orthogonal, n = 5 105 323 529 742 949 Grouping, Co-Chan, n = 5 102
320 524 736 941
[0058] To compare the performance of the CBS profit maximization
algorithm to the distance-based grouping scheme, two scenarios are
considered, namely, the cases of sufficient and insufficient
offered spectrum. For the case of sufficient spectrum, equation
(21) is utilized to find the total profit of the CBS. The shadowing
parameter of the desired FSU is m.sub.sd=4.23 (corresponds to a
shadow spread of 4 dB) and the multipath fading parameter for the
desired FSU is m.sub.md=2. The shadowing and the multipath fading
parameters for each interfering FSU are assumed to be m.sub.si=2,
m.sub.mi=4, respectively. The penetration loss is fixed at 15 dB,
and the target BER is 10.sup.-6. The offered price per channel is
c=20, and the cost paid by each FSU to the CBS is c.sub.b=1. Only
one FSU per FBS is assumed in the simulations. The noise power
spectral density is -174 dBm/Hz, and the bandwidth of each channel
is 200 KHz. The outage threshold is fixed at 10.sup.-3, and the SIR
threshold is fixed at 10 dB.
[0059] Plots 400a, 400b, and 400c of FIGS. 4A, 4B, and 4C,
respectively, show the expected CBS profit, normalized by the
channel bandwidth, against the FBS density in the network for n=3,
4, and 5, respectively. For n=3 (implies severe interference
conditions and high interference-free spectrum efficiency), the
cases of no grouping and grouping using the profit maximization
scheme both perform much better than the case of distance-based
grouping. This happens because the distance-based grouping scheme
is aimed at minimizing the required number of channels while
ensuring some minimum required QoS, and it does not observe the CBS
profit. In particular, it tries to reduce the number of groups by
assigning more members to each group, which, under severe
interference conditions, results in a very low profit from each
channel. For less severe interference conditions (larger path loss
exponent), as shown in FIG. 4B, the distance-based grouping scheme
outperforms the case of no grouping in terms of profit, since
adding more members does not affect the SIR significantly in this
case, but still the profit maximization scheme achieves the best
profit. Finally, for n=5, the distance-based grouping scheme
outperforms the greedy algorithm because it focuses on reducing the
number of groups and the interference effect may almost be ignored
in this case.
[0060] In plot 500 of FIG. 5, the uplink outage probability
performance of the profit maximization scheme is compared to that
of the distance-based scheme, where it can be easily noticed that
the distance-based grouping scheme outperforms the profit
maximization scheme, which makes it a better candidate for
QoS-guaranteed applications. To compare the performance of the CBS
profit maximization algorithm to the distance-based grouping scheme
under spectrum insufficiency scenarios, equation (27) is utilized
to obtain the profit of the CBS where the total number of channels
offered by the PU networks is B=100, and the price of each channel
is raised to 25. Plot 600a of FIG. 6A shows the normalized CBS
profit for n=3, wherein the same can be observed regarding the
total CBS profit resulting from the distance-based grouping, as
compared to the one resulting from the profit maximization grouping
and the no-grouping cases, except for the limit on the profit of
both the profit maximization grouping and the no-grouping cases,
which is caused by the limited number of channels offered from the
PU networks.
[0061] What is really interesting is what can be observed for the
cases of n=4 and n=5 (plots 600b and 600c of FIGS. 6B and 6C,
respectively). For large values of the path loss exponent, and due
to the limit on the number of channels to be purchased, the CBS
will get a relatively small profit or it will lose if no grouping
scheme is utilized. Furthermore, it can be noticed that the
resultant number of groups for the distance-based grouping scheme
is larger, which is reflected on the faster saturation of the CBS
profit for the distance-based grouping scheme, as compared to the
profit maximization scheme.
[0062] Plot 700 of FIG. 7 shows the CBS profit maximization
algorithm with orthogonal channel deployment and co-channel
deployment (i.e., when the MSUs are added to the groups of FSUs)
for different values of the path loss exponent n. The same set of
parameters is used as in the previous figures, except for the
existence of the MSUs. The FBSs constitutes 60% of the total number
of MSUs and FBSs in the network. It can be noticed that adding the
MSUs to the groups of FSUs does not always help to increase the
profit of the CBS.
[0063] What has been disclosed are two schemes for enhancing
spectrum efficiency, and thus reducing spectrum costs for cognitive
radio networks, namely, the distance-based and the
profit-maximization grouping schemes. The distance-based grouping
scheme hinges on grouping the FBSs based on the distances between
them into non-interfering groups and purchasing the amount of
spectrum sufficient to serve the groups. On the other hand, the
profit maximization scheme aims to maximize the profit of the CBS
by examining whether adding a SU to a group will increase the total
profit or not. The profit maximization scheme shows better
performance than the distance-based scheme in terms of achieving
higher total profit for the CBS, except for the case of slight
interference level under sufficient spectrum scenario, but at the
cost of worse uplink outage probability performance. Furthermore,
the co-channel deployment extension for the distance-based grouping
scheme results in a reduction in the number of channels to be
purchased from the PU networks. One the other hand, the co-channel
deployment extension of the profit maximization scheme does not
always reduce the number of purchased channels.
[0064] It is to be understood that the present invention is not
limited to the embodiments described above, but encompasses any and
all embodiments within the scope of the following claims.
* * * * *